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Lesson 1 of 8

Read binary and choose a width

Separate numeric value, written representation, and the width of the type.

Understand the idea

Bit k contributes 2^k to an unsigned integer. Decimal 13 and binary 1101 describe the same value: 8 + 4 + 1. Leading zero bits change the written width, not the value. A mask uses these positions to represent presence or a choice.

Trace a small example

13 has three set bits, highest set-bit index 3, and bit width 4. These are different quantities. Use an unsigned type for masks and a typed one such as 1ULL before shifting; an ordinary 1 is an int even if its result is assigned to a wider variable.

Conditions and cost

A shift count must be at least zero and less than the width of the promoted left operand. Never shift by the type width. Zero needs separate handling for formulas that assume a highest set bit.

Pause & predict

What is the value of binary 10110?

Choose an answer
Try it yourself

Turn the idea into code

Write 37 in binary and name its set-bit indices.

Give me a hint

Subtract powers of two from largest to smallest.

Show the explained solution

37 = 32 + 4 + 1 = binary 100101. The set-bit indices are 5, 2, and 0.

Your notes

Ready for the next idea?

Mark complete when you can explain it yourself.

From a problem to a programIdentify the input, output, and constraints, then translate a small plan into C++.Variables, types, and remembered valuesChoose a representation, initialize it, and understand what assignment really changes.Arithmetic without surprisesPredict division and remainder, widen before multiplication, and format decimal answers.Conditions and logical decisionsBuild exclusive categories, combine comparisons, and protect operations with short-circuit logic.Optional: other ways to chooseRecognize switch for exact choices and the conditional operator for choosing a value.For loops: make repetition preciseTrace initialization, condition, body, and update—and avoid an extra iteration.While, do-while, and stopping rulesChoose a loop from its stopping condition and read the exact input format.Break, continue, and early answersDistinguish leaving a loop from skipping one iteration, without losing required input.Five patterns worth understandingUse sums, counts, best-so-far candidates, products, and flags to process a stream.Nested loops: rows and columnsTranslate a shape into two loop roles and count the total work.Take a number apart, one digit at a timeUse remainder and division to process decimal digits, including zero.Multiple cases and a debugging mindsetCombine the patterns, isolate each case, and test the boundaries that can break your idea.Arrays: give every value a placeUnderstand indices, initialization, capacity, active length, and the first safe array loop.Scan, count, search, and compareDistinguish values from positions and preserve the exact tie rule a problem asks for.Change a sequence without losing itUpdate, copy, compare, reverse, and inspect neighbours using the correct bounds.Matrices: think in two coordinatesTraverse tables, total rows and columns, inspect diagonals, and protect grid neighbours.Characters become stringsSeparate characters from numbers, then safely inspect and edit managed text.Read the text the problem actually givesChoose words or full lines, preserve empty cases, and reset only the state that needs it.Scan text: count, filter, transformBuild a result from matching characters without losing leading zeros or skipping shifted text.Join, compare, and find textLearn content comparison, lexicographical order, substring counts, and the not-found sentinel.